Find the missing numerators in fraction addition problems on this math worksheet.

To solve the problem of finding the missing numerators in each equation, we need to determine what number should replace the blank (□) so that the equation holds true. Let's go through each equation step by step.

General Approach:

1. Identify the denominators: Ensure the denominators are the same on both sides of the equation.
2. Set up the equation: Write the equation with the unknown numerator as a variable.
3. Solve for the unknown numerator.

---

Detailed Solutions:

#### Row 1:
1. Equation 1:
\[
\frac{1}{6} + \frac{\square}{6} = \frac{2}{3}
\]
- Combine the fractions on the left side:
\[
\frac{1 + \square}{6} = \frac{2}{3}
\]
- Cross-multiply to solve for \(\square\):
\[
3(1 + \square) = 6 \cdot 2
\]
\[
3 + 3\square = 12
\]
\[
3\square = 9
\]
\[
\square = 3
\]

2. Equation 2:
\[
\frac{1}{10} + \frac{\square}{10} = \frac{2}{5}
\]
- Combine the fractions on the left side:
\[
\frac{1 + \square}{10} = \frac{2}{5}
\]
- Cross-multiply to solve for \(\square\):
\[
5(1 + \square) = 10 \cdot 2
\]
\[
5 + 5\square = 20
\]
\[
5\square = 15
\]
\[
\square = 3
\]

#### Row 2:
3. Equation 3:
\[
\frac{1}{4} + \frac{\square}{4} = \frac{1}{2}
\]
- Combine the fractions on the left side:
\[
\frac{1 + \square}{4} = \frac{1}{2}
\]
- Cross-multiply to solve for \(\square\):
\[
2(1 + \square) = 4 \cdot 1
\]
\[
2 + 2\square = 4
\]
\[
2\square = 2
\]
\[
\square = 1
\]

4. Equation 4:
\[
\frac{1}{12} + \frac{\square}{12} = \frac{1}{3}
\]
- Combine the fractions on the left side:
\[
\frac{1 + \square}{12} = \frac{1}{3}
\]
- Cross-multiply to solve for \(\square\):
\[
3(1 + \square) = 12 \cdot 1
\]
\[
3 + 3\square = 12
\]
\[
3\square = 9
\]
\[
\square = 3
\]

5. Equation 5:
\[
\frac{6}{18} + \frac{\square}{18} = \frac{1}{2}
\]
- Combine the fractions on the left side:
\[
\frac{6 + \square}{18} = \frac{1}{2}
\]
- Cross-multiply to solve for \(\square\):
\[
2(6 + \square) = 18 \cdot 1
\]
\[
12 + 2\square = 18
\]
\[
2\square = 6
\]
\[
\square = 3
\]

#### Row 3:
6. Equation 6:
\[
\frac{1}{10} + \frac{\square}{10} = \frac{1}{2}
\]
- Combine the fractions on the left side:
\[
\frac{1 + \square}{10} = \frac{1}{2}
\]
- Cross-multiply to solve for \(\square\):
\[
2(1 + \square) = 10 \cdot 1
\]
\[
2 + 2\square = 10
\]
\[
2\square = 8
\]
\[
\square = 4
\]

7. Equation 7:
\[
\frac{1}{8} + \frac{\square}{8} = \frac{1}{2}
\]
- Combine the fractions on the left side:
\[
\frac{1 + \square}{8} = \frac{1}{2}
\]
- Cross-multiply to solve for \(\square\):
\[
2(1 + \square) = 8 \cdot 1
\]
\[
2 + 2\square = 8
\]
\[
2\square = 6
\]
\[
\square = 3
\]

8. Equation 8:
\[
\frac{2}{6} + \frac{\square}{6} = \frac{2}{3}
\]
- Combine the fractions on the left side:
\[
\frac{2 + \square}{6} = \frac{2}{3}
\]
- Cross-multiply to solve for \(\square\):
\[
3(2 + \square) = 6 \cdot 2
\]
\[
6 + 3\square = 12
\]
\[
3\square = 6
\]
\[
\square = 2
\]

#### Row 4:
9. Equation 9:
\[
\frac{1}{6} + \frac{\square}{6} = \frac{1}{3}
\]
- Combine the fractions on the left side:
\[
\frac{1 + \square}{6} = \frac{1}{3}
\]
- Cross-multiply to solve for \(\square\):
\[
3(1 + \square) = 6 \cdot 1
\]
\[
3 + 3\square = 6
\]
\[
3\square = 3
\]
\[
\square = 1
\]

10. Equation 10:
\[
\frac{2}{15} + \frac{\square}{15} = \frac{1}{3}
\]
- Combine the fractions on the left side:
\[
\frac{2 + \square}{15} = \frac{1}{3}
\]
- Cross-multiply to solve for \(\square\):
\[
3(2 + \square) = 15 \cdot 1
\]
\[
6 + 3\square = 15
\]
\[
3\square = 9
\]
\[
\square = 3
\]

11. Equation 11:
\[
\frac{5}{12} + \frac{\square}{12} = \frac{2}{3}
\]
- Combine the fractions on the left side:
\[
\frac{5 + \square}{12} = \frac{2}{3}
\]
- Cross-multiply to solve for \(\square\):
\[
3(5 + \square) = 12 \cdot 2
\]
\[
15 + 3\square = 24
\]
\[
3\square = 9
\]
\[
\square = 3
\]

#### Row 5:
12. Equation 12:
\[
\frac{5}{10} + \frac{\square}{10} = \frac{4}{5}
\]
- Combine the fractions on the left side:
\[
\frac{5 + \square}{10} = \frac{4}{5}
\]
- Cross-multiply to solve for \(\square\):
\[
5(5 + \square) = 10 \cdot 4
\]
\[
25 + 5\square = 40
\]
\[
5\square = 15
\]
\[
\square = 3
\]

13. Equation 13:
\[
\frac{3}{8} + \frac{\square}{8} = \frac{3}{4}
\]
- Combine the fractions on the left side:
\[
\frac{3 + \square}{8} = \frac{3}{4}
\]
- Cross-multiply to solve for \(\square\):
\[
4(3 + \square) = 8 \cdot 3
\]
\[
12 + 4\square = 24
\]
\[
4\square = 12
\]
\[
\square = 3
\]

14. Equation 14:
\[
\frac{2}{20} + \frac{\square}{20} = \frac{1}{4}
\]
- Combine the fractions on the left side:
\[
\frac{2 + \square}{20} = \frac{1}{4}
\]
- Cross-multiply to solve for \(\square\):
\[
4(2 + \square) = 20 \cdot 1
\]
\[
8 + 4\square = 20
\]
\[
4\square = 12
\]
\[
\square = 3
\]

#### Row 6:
15. Equation 15:
\[
\frac{9}{20} + \frac{\square}{20} = \frac{3}{4}
\]
- Combine the fractions on the left side:
\[
\frac{9 + \square}{20} = \frac{3}{4}
\]
- Cross-multiply to solve for \(\square\):
\[
4(9 + \square) = 20 \cdot 3
\]
\[
36 + 4\square = 60
\]
\[
4\square = 24
\]
\[
\square = 6
\]

16. Equation 16:
\[
\frac{1}{8} + \frac{\square}{8} = \frac{1}{4}
\]
- Combine the fractions on the left side:
\[
\frac{1 + \square}{8} = \frac{1}{4}
\]
- Cross-multiply to solve for \(\square\):
\[
4(1 + \square) = 8 \cdot 1
\]
\[
4 + 4\square = 8
\]
\[
4\square = 4
\]
\[
\square = 1
\]

17. Equation 17:
\[
\frac{1}{16} + \frac{\square}{16} = \frac{1}{4}
\]
- Combine the fractions on the left side:
\[
\frac{1 + \square}{16} = \frac{1}{4}
\]
- Cross-multiply to solve for \(\square\):
\[
4(1 + \square) = 16 \cdot 1
\]
\[
4 + 4\square = 16
\]
\[
4\square = 12
\]
\[
\square = 3
\]

#### Row 7:
18. Equation 18:
\[
\frac{2}{9} + \frac{\square}{9} = \frac{1}{3}
\]
- Combine the fractions on the left side:
\[
\frac{2 + \square}{9} = \frac{1}{3}
\]
- Cross-multiply to solve for \(\square\):
\[
3(2 + \square) = 9 \cdot 1
\]
\[
6 + 3\square = 9
\]
\[
3\square = 3
\]
\[
\square = 1
\]

19. Equation 19:
\[
\frac{7}{25} + \frac{\square}{25} = \frac{3}{5}
\]
- Combine the fractions on the left side:
\[
\frac{7 + \square}{25} = \frac{3}{5}
\]
- Cross-multiply to solve for \(\square\):
\[
5(7 + \square) = 25 \cdot 3
\]
\[
35 + 5\square = 75
\]
\[
5\square = 40
\]
\[
\square = 8
\]

20. Equation 20:
\[
\frac{3}{9} + \frac{\square}{9} = \frac{2}{3}
\]
- Combine the fractions on the left side:
\[
\frac{3 + \square}{9} = \frac{2}{3}
\]
- Cross-multiply to solve for \(\square\):
\[
3(3 + \square) = 9 \cdot 2
\]
\[
9 + 3\square = 18
\]
\[
3\square = 9
\]
\[
\square = 3
\]

---

Final Answer:

\[
\boxed{
\begin{array}{ccc}
3 & 3 & \\
1 & 3 & 3 \\
4 & 3 & 2 \\
1 & 3 & 3 \\
3 & 3 & 6 \\
1 & 1 & 3 \\
1 & 8 & 3 \\
\end{array}
}
\]